%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG072+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:25:23 AM UTC 2026
% Result : Theorem 156.34s 80.77s
% Output : Refutation 156.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 154 ( 17 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 560 ( 82 ~; 62 |; 24 &; 386 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(xR_decl,type,
xR: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xP_decl,type,
xP: $i ).
thf(aScalar0_decl,type,
aScalar0: $i > $o ).
thf(sz0z00_decl,type,
sz0z00: $i ).
thf(xE_decl,type,
xE: $i ).
thf(xC_decl,type,
xC: $i ).
thf(xD_decl,type,
xD: $i ).
thf(xH_decl,type,
xH: $i ).
thf(xF_decl,type,
xF: $i ).
thf(xG_decl,type,
xG: $i ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( B @ aScalar0 )
& ( A @ aScalar0 ) )
=> ( B @ ( A @ sdtpldt0 ) @ aScalar0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
thf(234,plain,
! [A: $i,B: $i] :
( ( ( B @ aScalar0 )
& ( A @ aScalar0 ) )
=> ( B @ ( A @ sdtpldt0 ) @ aScalar0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sdtpldt0 ) @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(cnf,[status(esa)],[234]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ aScalar0 )
& ( C @ aScalar0 )
& ( B @ aScalar0 )
& ( A @ aScalar0 ) )
=> ( ( ( D @ ( C @ sdtlseqdt0 ) )
& ( C @ ( sz0z00 @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( D @ ( B @ sdtasdt0 ) @ ( C @ ( A @ sdtasdt0 ) @ sdtlseqdt0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
thf(187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ aScalar0 )
& ( C @ aScalar0 )
& ( B @ aScalar0 )
& ( A @ aScalar0 ) )
=> ( ( ( D @ ( C @ sdtlseqdt0 ) )
& ( C @ ( sz0z00 @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( D @ ( B @ sdtasdt0 ) @ ( C @ ( A @ sdtasdt0 ) @ sdtlseqdt0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ sdtasdt0 ) @ ( C @ ( A @ sdtasdt0 ) @ sdtlseqdt0 ) )
| ~ ( D @ ( C @ sdtlseqdt0 ) )
| ~ ( C @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( D @ aScalar0 )
| ~ ( C @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(cnf,[status(esa)],[187]) ).
thf(1,conjecture,
xP @ ( xP @ sdtpldt0 ) @ ( xP @ ( xP @ sdtpldt0 ) @ sdtasdt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtasdt0 ) @ sdtlseqdt0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( xP @ ( xP @ sdtpldt0 ) @ ( xP @ ( xP @ sdtpldt0 ) @ sdtasdt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtasdt0 ) @ sdtlseqdt0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
~ ( xP @ ( xP @ sdtpldt0 ) @ ( xP @ ( xP @ sdtpldt0 ) @ sdtasdt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtasdt0 ) @ sdtlseqdt0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ sdtasdt0 ) @ ( C @ ( A @ sdtasdt0 ) @ sdtlseqdt0 ) )
!= ( xP @ ( xP @ sdtpldt0 ) @ ( xP @ ( xP @ sdtpldt0 ) @ sdtasdt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtasdt0 ) @ sdtlseqdt0 ) ) )
| ~ $true
| ~ ( D @ ( C @ sdtlseqdt0 ) )
| ~ ( C @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( D @ aScalar0 )
| ~ ( C @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(paramod_ordered,[status(thm)],[188,65]) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ sdtasdt0 ) @ ( C @ ( A @ sdtasdt0 ) @ sdtlseqdt0 ) )
!= ( xP @ ( xP @ sdtpldt0 ) @ ( xP @ ( xP @ sdtpldt0 ) @ sdtasdt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtasdt0 ) @ sdtlseqdt0 ) ) )
| ~ ( D @ ( C @ sdtlseqdt0 ) )
| ~ ( C @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( D @ aScalar0 )
| ~ ( C @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(simp,[status(thm)],[310]) ).
thf(312,plain,
( ~ ( xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ) )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( xS @ ( xR @ sdtpldt0 ) )),bind(B,$thf( xP @ ( xP @ sdtpldt0 ) )),bind(C,$thf( xS @ ( xR @ sdtpldt0 ) )),bind(D,$thf( xP @ ( xP @ sdtpldt0 ) ))]]) ).
thf(401,plain,
( ~ ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(simp,[status(thm)],[312]) ).
thf(445,plain,
( ~ $true
| ( ( xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ) )
!= ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(eqfactor_ordered,[status(thm)],[401]) ).
thf(451,plain,
( ( ( xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ) )
!= ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(simp,[status(thm)],[445]) ).
thf(53,axiom,
xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2610) ).
thf(246,plain,
xP @ ( xP @ sdtpldt0 ) @ ( xS @ ( xR @ sdtpldt0 ) @ sdtlseqdt0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(56,axiom,
( ( xP @ ( xP @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
& ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2628) ).
thf(267,plain,
( ( xP @ ( xP @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
& ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(268,plain,
( ( xP @ ( xP @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
& ( xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
inference(cnf,[status(esa)],[267]) ).
thf(269,plain,
xS @ ( xR @ sdtpldt0 ) @ ( sz0z00 @ sdtlseqdt0 ),
inference(cnfConj,[status(thm)],[268]) ).
thf(160898,plain,
( ~ $true
| ~ $true
| ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(rewrite,[status(thm)],[451,246,269]) ).
thf(160899,plain,
( ~ ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) ),
inference(simp,[status(thm)],[160898]) ).
thf(161149,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aScalar0 )
!= ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 ) )
| ~ $true
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(paramod_ordered,[status(thm)],[235,160899]) ).
thf(161150,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aScalar0 )
!= ( xP @ ( xP @ sdtpldt0 ) @ aScalar0 ) )
| ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(simp,[status(thm)],[161149]) ).
thf(161151,plain,
( ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ ( xP @ aScalar0 )
| ~ ( xP @ aScalar0 ) ),
inference(pattern_uni,[status(thm)],[161150:[bind(A,$thf( xP )),bind(B,$thf( xP ))]]) ).
thf(161353,plain,
( ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ ( xP @ aScalar0 ) ),
inference(simp,[status(thm)],[161151]) ).
thf(61,axiom,
( ( xP
= ( xH @ ( xE @ sdtasdt0 ) ) )
& ( xP @ aScalar0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
thf(279,plain,
( ( xP
= ( xH @ ( xE @ sdtasdt0 ) ) )
& ( xP @ aScalar0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(280,plain,
( ( xP
= ( xH @ ( xE @ sdtasdt0 ) ) )
& ( xP @ aScalar0 ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
xP @ aScalar0,
inference(cnfConj,[status(thm)],[280]) ).
thf(164797,plain,
( ~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 )
| ~ $true ),
inference(rewrite,[status(thm)],[161353,281]) ).
thf(164798,plain,
~ ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ),
inference(simp,[status(thm)],[164797]) ).
thf(164922,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aScalar0 )
!= ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) )
| ~ $true
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(paramod_ordered,[status(thm)],[235,164798]) ).
thf(164923,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ aScalar0 )
!= ( xS @ ( xR @ sdtpldt0 ) @ aScalar0 ) )
| ~ ( B @ aScalar0 )
| ~ ( A @ aScalar0 ) ),
inference(simp,[status(thm)],[164922]) ).
thf(164924,plain,
( ~ ( xS @ aScalar0 )
| ~ ( xR @ aScalar0 ) ),
inference(pattern_uni,[status(thm)],[164923:[bind(A,$thf( xR )),bind(B,$thf( xS ))]]) ).
thf(49,axiom,
( ( xR
= ( xG @ ( xC @ sdtasdt0 ) ) )
& ( xR @ aScalar0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
thf(236,plain,
( ( xR
= ( xG @ ( xC @ sdtasdt0 ) ) )
& ( xR @ aScalar0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(237,plain,
( ( xR
= ( xG @ ( xC @ sdtasdt0 ) ) )
& ( xR @ aScalar0 ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
xR @ aScalar0,
inference(cnfConj,[status(thm)],[237]) ).
thf(41,axiom,
( ( xS
= ( xD @ ( xF @ sdtasdt0 ) ) )
& ( xS @ aScalar0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
thf(205,plain,
( ( xS
= ( xD @ ( xF @ sdtasdt0 ) ) )
& ( xS @ aScalar0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(206,plain,
( ( xS
= ( xD @ ( xF @ sdtasdt0 ) ) )
& ( xS @ aScalar0 ) ),
inference(cnf,[status(esa)],[205]) ).
thf(207,plain,
xS @ aScalar0,
inference(cnfConj,[status(thm)],[206]) ).
thf(165037,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[164924,238,207]) ).
thf(165038,plain,
$false,
inference(simp,[status(thm)],[165037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG072+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n008.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 05:59:09 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.20 % [INFO] Parsing done (232ms).
% 1.56/1.21 % [INFO] Running in sequential loop mode.
% 2.28/1.60 % [INFO] eprover registered as external prover.
% 2.28/1.61 % [INFO] Scanning for conjecture ...
% 2.49/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ...
% 2.69/1.83 % [INFO] Axiom selection finished. Selected 62 axioms (removed 0 axioms).
% 2.69/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.93/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.93/1.94 % [INFO] Type checking passed.
% 2.93/1.95 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 156.34/80.77 % [INFO] Killing All external provers ...
% 156.34/80.77 % Time passed: 80226ms (effective reasoning time: 79547ms)
% 156.34/80.77 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 156.34/80.77 % Axioms used in derivation (7): m__2628, m__1930, m__2610, mLEMonM, m__1911, mSumSc, m__1892
% 156.34/80.77 % No. of inferences in proof: 46
% 156.34/80.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 80226 ms resp. 79547 ms w/o parsing
% 156.58/80.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 156.58/80.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------